How many years will $ 100 takes to grow to $672.75 if you invested it 10% interest compounded annually?

To solve this problem, we can use the formula for compound interest, which is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

In this case, we are trying to find t (time), so we will need to rearrange the formula to solve for t. The given values are:

A = $672.75 P =$100 r = 10% = 0.10 (in decimal form) n = 1 (since the interest is compounded annually)

Substituting these values into the formula, we get:

672.75 = 100(1 + 0.10/1)^(1*t)

Solving for t, we get:

t = ln(672.75/100) / (1 * ln(1 + 0.10/1))

Using a calculator to compute the natural logarithm (ln), we find:

t = ln(6.7275) / ln(1.1) ≈ 18.53 years

So, it will take approximately 18.53 years for $100 to grow to$672.75 if invested at 10% interest compounded annually.